The document proposes an attribute-based storage system that supports secure deduplication of encrypted data in cloud computing. It uses ciphertext-policy attribute-based encryption (CP-ABE) which allows data to be encrypted for access by users with specific attributes, avoiding duplicate storage. A private cloud performs duplicate detection and regeneration of ciphertexts for the same data under different access policies, while a public cloud stores the data. This ensures secure data sharing and prevents wasted storage from duplicative encrypted copies of the same data.